Being a nonlinear operator,fractional derivatives can affect the enforcement of existence at any given time.As a result,the memory effect has an impact on all nonlinear processes modeled by fractional order differenti...Being a nonlinear operator,fractional derivatives can affect the enforcement of existence at any given time.As a result,the memory effect has an impact on all nonlinear processes modeled by fractional order differential equations(FODEs).The goal of this study is to increase the fractional model of the TB virus’s(FMTBV)accuracy.Stochastic solvers have never been used to solve FMTBV previously.The Bayesian regularized artificial(BRA)method and neural networks(NNs),often referred to as BRA-NNs,were used to solve the FMTBV model.Each scenario features five occurrences that each reflect a different order of derivatives,ranging from 0.8,0.85,0.9,0.95,and 1,as well as five potential rates for different parameters.Training data made up 90%of the data,testing data made up 5%,and validation data made up 5%of the data used to illustrate the FMTBV’s approximations.To verify that the BRA-NNs were correct,the generated simulations were described in the following solutions using the FOLotkaVolterra approach in MATLAB.Comprehensive Simulink results in terms of mean square error,error histogram,and regression analysis investigations further highlight the competence,dependability,and accuracy of the suggested BRA-NNs.展开更多
A Recent paper by Ma et al.,claims to estimate the state of charge of Lithium-ion batteries with a fractionalorder impedance model including a Warburg and a constant phase element(CPE)with a maximum error of 0.5%[1].T...A Recent paper by Ma et al.,claims to estimate the state of charge of Lithium-ion batteries with a fractionalorder impedance model including a Warburg and a constant phase element(CPE)with a maximum error of 0.5%[1].The proposed equivalent circuit model from[1]is reproduced in Fig.1.展开更多
Recently, a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantage...Recently, a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantages over the preceding definitions. For mathematical models in applied sciences and to preserve the dimensionality of the physical quantities, an auxiliary parameter （~r） which has the dimension of seconds should be implemented in the fractional derivative definition. We obtain analytic solutions for the resulting conformable fractional differential equations describing the vertical velocity and the height of the falling body. It is shown that the dimensions of velocity and height are always correct without any restrictions on the auxiliary parameter cr which contradicts with the results in the literature when applying the Caputo definition to the same problem. This may open the door for many future works either to describe the role of such an auxiliary parameter or to derive a more suitable definition for the fractional derivative.展开更多
This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstruc...This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstructural degradation is decomposed into two parts:an instantaneous part arising from monotonic loading and a fatigue-related one induced by cyclic loading,relating to the initiation and propagation of microcracks.The inelastic deformation arises directly from frictional sliding along microcracks,inherently coupled with the damage effect.A fractional plastic flow rule is introduced using stress-fractional plasticity operations and covariant transformation approach,instead of classical plastic flow function.Additionally,the progression of fatigue damage is intricately tied to subcracks and can be calculated through application of a convolution law.The number of loading cycles serves as an integration variable,establishing a connection between inelastic deformation and the evolution of fatigue damage.In order to verify the accuracy of the proposed model,comparison between analytical solutions and experimental data are carried out on three different rocks subjected to conventional triaxial compression and cyclic loading tests.The evolution of damage variables is also investigated along with the cumulative deformation and fatigue lifetime.The improvement of the fractional model is finally discussed by comparing with an existing associated fatigue model in literature.展开更多
In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6...In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.展开更多
Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensiona...Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.展开更多
This paper develops an Ito-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters H∈(1/3,1/2],using the Lyons'rough path framework.This approach is designed to fill gaps ...This paper develops an Ito-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters H∈(1/3,1/2],using the Lyons'rough path framework.This approach is designed to fill gaps in conventional stochastic calculus models that fail to account for temporal persistence prevalent in dynamic systems such as those found in economics,finance,and engineering.The pathwise-defined method not only meets the zero expectation criterion but also addresses the challenges of integrating non-semimartingale processes,which traditional Ito calculus cannot handle.We apply this theory to fractional Black–Scholes models and high-dimensional fractional Ornstein–Uhlenbeck processes,illustrating the advantages of this approach.Additionally,the paper discusses the generalization of It?integrals to rough differential equations(RDE)driven by f BM,emphasizing the necessity of integrand-specific adaptations in the It?rough path lift for stochastic modeling.展开更多
In the early stages of oil exploration,oil is produced through processes such as well drilling.Later,hot water may be injected into the well to improve production.A key challenge is understanding how the temperature a...In the early stages of oil exploration,oil is produced through processes such as well drilling.Later,hot water may be injected into the well to improve production.A key challenge is understanding how the temperature and velocity of the injected hot water affect the production rate.This is the focus of the current study.It proposes variableviscosity mathematical models for heat and water saturation in a reservoir containing Bonny-light crude oil,with the aim of investigating the effects of water temperature and velocity on the recovery rate.First,two sets of experimental data are used to construct explicit temperature-dependent viscosity models for Bonny-light crude oil and water.These viscosity models are incorporated into the Buckley-Leverette equation for the dynamics of water saturation.A convex combination of the thermal conductivities of oil and water is used to formulate a heat propagation model.A finite volume scheme with temperature-dependent HLL numerical flux is proposed for saturation,while a finite difference approximation is derived for the heat model,both on a staggered grid.The convergence of the method is verified numerically.Simulations are conducted with different parameter values.The results show that at a wall temperature of 10℃,an increase in the injection velocity from 0.1 to 0.25 increases the production rate from 8.33%to 20.8%.Meanwhile,with an injection velocity of v=1,an increase in the temperature of the injected water from 25℃ to 55℃ increases production rate from 59.48%to 61.95%.Therefore,it is concluded that an increase in either or both the temperature and velocity of the injected water leads to increased oil production,which is physically realistic.This indicates that the developed model is able to give useful insights into hot water flooding.展开更多
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the frac...The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.展开更多
The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases ...The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.展开更多
State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have p...State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have provided a distinct insight into SOC estimation.In this article,we compare five state-of-the-art FOMs in terms of SOC estimation.To this end,firstly,characterisation tests on lithium ion batteries are conducted,and the experimental results are used to identify FOM parameters.Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy.The model R(RQ)W shows superior identification accuracy than the other four FOMs.Secondly,the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles,memory lengths,ambient temperatures,cells and voltage/current drifts.The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs.Although more complex models can have better robustness against temperature variation,R(RQ),the simplest FOM,can overall provide satisfactory accuracy.Validation results on different cells demonstrate the generalisation ability of FOMs,and R(RQ)outperforms other models.Moreover,R(RQ)shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.展开更多
To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and...To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.展开更多
In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and t...We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.展开更多
Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on ...Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.展开更多
The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected...The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected by COVID-19. The world is now facing a drastic situation because of this ongoing virus. Bangladesh is also dealing with this issue, and due to its dense population, it is particularly vulnerable to the spread of COVID-19. Recently, many non-linear systems have been proposed to solve the SIR (Susceptible, Infected, and Recovered) model for predicting Coronavirus cases. In this paper, we have discussed the fractional order SIR epidemic model of a non-fatal disease in a population of a constant size. Using the Laplace Adomian Decomposition method, we get an approximate solution to the model. To predict the dynamic transmission of COVID-19 in Bangladesh, we provide a numerical argument based on real data. We also conducted a comparative analysis among susceptible, infected, and recovered people. Furthermore, the most sensitive parameters for the Basic Reproduction Number (<em>R</em><sub>0</sub>) are graphically presented, and the impact of the compartments on the transmission dynamics of the COVID-19 pandemic is thoroughly investigated.展开更多
In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themas...In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.展开更多
In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of...In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.展开更多
The motion of pore water directly influences mechanical properties of soils, which are variable during creep. Accurate description of the evolution of mechanical properties of soils can help to reveal the internal beh...The motion of pore water directly influences mechanical properties of soils, which are variable during creep. Accurate description of the evolution of mechanical properties of soils can help to reveal the internal behavior of pore water. Based on the idea of using the fractional order to reflect mechanical properties of soils, a fractional creep model is proposed by introducing a variable-order fractional operator, and realized on a series of creep responses in soft soils. A comparative analysis illustrates that the evolution of mechanical properties, shown through the simulated results, exactly corresponds to the motion of pore water and the solid skeleton. This demonstrates that the proposed variable-order fractional model can be employed to characterize the evolution of mechanical properties of and the pore water motion in soft soils during creep. It is observed that the fractional order from the proposed model is related to the dissipation rate of pore water pressure.展开更多
This paper presents a comprehensive study of disease spreading dynamics through the application of a nonlinear fractional order epidemic SEIRS model.By incorporating the Crowley-Martin type functional response and a s...This paper presents a comprehensive study of disease spreading dynamics through the application of a nonlinear fractional order epidemic SEIRS model.By incorporating the Crowley-Martin type functional response and a saturated treatment function,the model effectively captures the intricacies of real-world epidemics.Our research establishes the existence,uniqueness,non-negativity and boundedness of the solution,while also investigating the model's fundamental reproduction number.Additionally,we conduct a thorough analysis of the specific conditions governing the local and global stability of the model's equilibriums.A notable observation is the variation of the reproduction number with the fractional-orderα,which represents a memory effect on individuals'dynamic behavior and reveals the infuence of interactions between compartments.To validate these theoretical findings,we employ numerical simulations using Matlab,demonstrating that inhibition measures for susceptibles and the saturated treatment parameters play a pivotal role in determining the disease state.Specifically,we observe that as these parameter values increase,the transition from endemic equilibrium to disease-free equilibrium occurs.展开更多
基金supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2024/R/1445).
文摘Being a nonlinear operator,fractional derivatives can affect the enforcement of existence at any given time.As a result,the memory effect has an impact on all nonlinear processes modeled by fractional order differential equations(FODEs).The goal of this study is to increase the fractional model of the TB virus’s(FMTBV)accuracy.Stochastic solvers have never been used to solve FMTBV previously.The Bayesian regularized artificial(BRA)method and neural networks(NNs),often referred to as BRA-NNs,were used to solve the FMTBV model.Each scenario features five occurrences that each reflect a different order of derivatives,ranging from 0.8,0.85,0.9,0.95,and 1,as well as five potential rates for different parameters.Training data made up 90%of the data,testing data made up 5%,and validation data made up 5%of the data used to illustrate the FMTBV’s approximations.To verify that the BRA-NNs were correct,the generated simulations were described in the following solutions using the FOLotkaVolterra approach in MATLAB.Comprehensive Simulink results in terms of mean square error,error histogram,and regression analysis investigations further highlight the competence,dependability,and accuracy of the suggested BRA-NNs.
文摘A Recent paper by Ma et al.,claims to estimate the state of charge of Lithium-ion batteries with a fractionalorder impedance model including a Warburg and a constant phase element(CPE)with a maximum error of 0.5%[1].The proposed equivalent circuit model from[1]is reproduced in Fig.1.
文摘Recently, a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantages over the preceding definitions. For mathematical models in applied sciences and to preserve the dimensionality of the physical quantities, an auxiliary parameter （~r） which has the dimension of seconds should be implemented in the fractional derivative definition. We obtain analytic solutions for the resulting conformable fractional differential equations describing the vertical velocity and the height of the falling body. It is shown that the dimensions of velocity and height are always correct without any restrictions on the auxiliary parameter cr which contradicts with the results in the literature when applying the Caputo definition to the same problem. This may open the door for many future works either to describe the role of such an auxiliary parameter or to derive a more suitable definition for the fractional derivative.
基金Fundamental Research Funds for the Central Universities(Grant No.B230201059)for the support.
文摘This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstructural degradation is decomposed into two parts:an instantaneous part arising from monotonic loading and a fatigue-related one induced by cyclic loading,relating to the initiation and propagation of microcracks.The inelastic deformation arises directly from frictional sliding along microcracks,inherently coupled with the damage effect.A fractional plastic flow rule is introduced using stress-fractional plasticity operations and covariant transformation approach,instead of classical plastic flow function.Additionally,the progression of fatigue damage is intricately tied to subcracks and can be calculated through application of a convolution law.The number of loading cycles serves as an integration variable,establishing a connection between inelastic deformation and the evolution of fatigue damage.In order to verify the accuracy of the proposed model,comparison between analytical solutions and experimental data are carried out on three different rocks subjected to conventional triaxial compression and cyclic loading tests.The evolution of damage variables is also investigated along with the cumulative deformation and fatigue lifetime.The improvement of the fractional model is finally discussed by comparing with an existing associated fatigue model in literature.
基金supported by the Fundacao para a Ciencia e Tecnologia,FCT,under the project https://doi.org/10.54499/UIDB/04674/2020(accessed on 1 January 2025).
文摘In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.
基金the financial support from the National Natural Science Foundation of China(No.52109119)the Guangxi Natural Science Foundation(No.2021GXNSFBA075030)+2 种基金the Guangxi Science and Technology Project(No.Guike AD20325002)the Chinese Postdoctoral Science Fund Project(No.2022 M723408)the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin(China Institute of Water Resources and Hydropower Research)(No.IWHR-SKL-202202).
文摘Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.
基金Supported by Shanghai Artificial Intelligence Laboratory。
文摘This paper develops an Ito-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters H∈(1/3,1/2],using the Lyons'rough path framework.This approach is designed to fill gaps in conventional stochastic calculus models that fail to account for temporal persistence prevalent in dynamic systems such as those found in economics,finance,and engineering.The pathwise-defined method not only meets the zero expectation criterion but also addresses the challenges of integrating non-semimartingale processes,which traditional Ito calculus cannot handle.We apply this theory to fractional Black–Scholes models and high-dimensional fractional Ornstein–Uhlenbeck processes,illustrating the advantages of this approach.Additionally,the paper discusses the generalization of It?integrals to rough differential equations(RDE)driven by f BM,emphasizing the necessity of integrand-specific adaptations in the It?rough path lift for stochastic modeling.
文摘In the early stages of oil exploration,oil is produced through processes such as well drilling.Later,hot water may be injected into the well to improve production.A key challenge is understanding how the temperature and velocity of the injected hot water affect the production rate.This is the focus of the current study.It proposes variableviscosity mathematical models for heat and water saturation in a reservoir containing Bonny-light crude oil,with the aim of investigating the effects of water temperature and velocity on the recovery rate.First,two sets of experimental data are used to construct explicit temperature-dependent viscosity models for Bonny-light crude oil and water.These viscosity models are incorporated into the Buckley-Leverette equation for the dynamics of water saturation.A convex combination of the thermal conductivities of oil and water is used to formulate a heat propagation model.A finite volume scheme with temperature-dependent HLL numerical flux is proposed for saturation,while a finite difference approximation is derived for the heat model,both on a staggered grid.The convergence of the method is verified numerically.Simulations are conducted with different parameter values.The results show that at a wall temperature of 10℃,an increase in the injection velocity from 0.1 to 0.25 increases the production rate from 8.33%to 20.8%.Meanwhile,with an injection velocity of v=1,an increase in the temperature of the injected water from 25℃ to 55℃ increases production rate from 59.48%to 61.95%.Therefore,it is concluded that an increase in either or both the temperature and velocity of the injected water leads to increased oil production,which is physically realistic.This indicates that the developed model is able to give useful insights into hot water flooding.
基金The project supported by the National Natural Science Foundation of China (10002003)Foundation for University Key Teacher by the Ministry of EducationResearch Fund for the Doctoral Program of Higher Education
文摘The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.
基金The project supported by the National Natural Science Foundation of China (10272067, 10426024)the Doctoral Program Foundation of the Education Ministry of China (20030422046)the Natural Science Foundation of Shandong University at Weihai.
文摘The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.
基金Beijing Municipal Natural Science Foundation of China(Grant No.3182035)National Natural Science Foundation of China(Grant No.51877009).
文摘State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have provided a distinct insight into SOC estimation.In this article,we compare five state-of-the-art FOMs in terms of SOC estimation.To this end,firstly,characterisation tests on lithium ion batteries are conducted,and the experimental results are used to identify FOM parameters.Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy.The model R(RQ)W shows superior identification accuracy than the other four FOMs.Secondly,the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles,memory lengths,ambient temperatures,cells and voltage/current drifts.The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs.Although more complex models can have better robustness against temperature variation,R(RQ),the simplest FOM,can overall provide satisfactory accuracy.Validation results on different cells demonstrate the generalisation ability of FOMs,and R(RQ)outperforms other models.Moreover,R(RQ)shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.
基金supported by the National Natural Science Foundation of China(5147915151279149+2 种基金71540027)the China Postdoctoral Science Foundation Special Foundation Project(2013T607552012M521487)
文摘To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project No. (PNURSP2022R14),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia。
文摘We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.
基金This work was supported in part by the National Science Foundation through Grant CNS-1726865by the USDA under Grant 2019-67021-28990.
文摘Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.
文摘The COVID-19 pandemic is a curse and a threat to global health, development, the economy, and peaceful society because of its massive transmission and high rates of mutation. More than 220 countries have been affected by COVID-19. The world is now facing a drastic situation because of this ongoing virus. Bangladesh is also dealing with this issue, and due to its dense population, it is particularly vulnerable to the spread of COVID-19. Recently, many non-linear systems have been proposed to solve the SIR (Susceptible, Infected, and Recovered) model for predicting Coronavirus cases. In this paper, we have discussed the fractional order SIR epidemic model of a non-fatal disease in a population of a constant size. Using the Laplace Adomian Decomposition method, we get an approximate solution to the model. To predict the dynamic transmission of COVID-19 in Bangladesh, we provide a numerical argument based on real data. We also conducted a comparative analysis among susceptible, infected, and recovered people. Furthermore, the most sensitive parameters for the Basic Reproduction Number (<em>R</em><sub>0</sub>) are graphically presented, and the impact of the compartments on the transmission dynamics of the COVID-19 pandemic is thoroughly investigated.
文摘In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.
文摘In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.
基金supported by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK2012810)the Fundamental Research Funds for the Central Universities(Grant No.2009B15114)
文摘The motion of pore water directly influences mechanical properties of soils, which are variable during creep. Accurate description of the evolution of mechanical properties of soils can help to reveal the internal behavior of pore water. Based on the idea of using the fractional order to reflect mechanical properties of soils, a fractional creep model is proposed by introducing a variable-order fractional operator, and realized on a series of creep responses in soft soils. A comparative analysis illustrates that the evolution of mechanical properties, shown through the simulated results, exactly corresponds to the motion of pore water and the solid skeleton. This demonstrates that the proposed variable-order fractional model can be employed to characterize the evolution of mechanical properties of and the pore water motion in soft soils during creep. It is observed that the fractional order from the proposed model is related to the dissipation rate of pore water pressure.
文摘This paper presents a comprehensive study of disease spreading dynamics through the application of a nonlinear fractional order epidemic SEIRS model.By incorporating the Crowley-Martin type functional response and a saturated treatment function,the model effectively captures the intricacies of real-world epidemics.Our research establishes the existence,uniqueness,non-negativity and boundedness of the solution,while also investigating the model's fundamental reproduction number.Additionally,we conduct a thorough analysis of the specific conditions governing the local and global stability of the model's equilibriums.A notable observation is the variation of the reproduction number with the fractional-orderα,which represents a memory effect on individuals'dynamic behavior and reveals the infuence of interactions between compartments.To validate these theoretical findings,we employ numerical simulations using Matlab,demonstrating that inhibition measures for susceptibles and the saturated treatment parameters play a pivotal role in determining the disease state.Specifically,we observe that as these parameter values increase,the transition from endemic equilibrium to disease-free equilibrium occurs.
